Manship, 27, posted a 3.08 ERA in 12 games with the Red Wings, including four starts. He struck out 25 and walked 15 in 38 innings.
The move gives the Twins 13 pitchers, which Twins manager Ron Gardenhire said was necessary because of recent overuse of his relievers with starters struggling to go deep in games.
"We needed pitching," Gardenhire said. "We had to have another pitcher because our bullpen is depleted. And Manship has been pitching well. He's been extended out and has been starting."
Manship was scheduled to start with Rochester on Sunday but was told by Red Wings manager Gene Glynn on Saturday that he would be headed to Minnesota. He is expected to be used in long relief, although Gardenhire wouldn't rule out the possibility of him making a spot start at some point.
"I'm definitely confident," said Manship, who has a career 5.63 ERA in 64 innings with the Twins. "My arm can handle multiple innings, which is good. I'm glad to see that I was able to go seven innings in my last outing. My arm has bounced back from last year, which is good."
Komatsu, meanwhile, didn't see much action with the Twins, batting .219 in 15 games, with his last start in the outfield coming on May 16.
Komatsu was acquired by the Twins via waivers from the Cardinals on May 4 after he was designated for assignment. He's a Rule 5 Draft pick from the Nationals, so if a team selects him off waivers from the Twins, they must keep him on their active roster all season or offer him back to Washington.
But if Komatsu clears waivers, the Nationals can take him back for $25,000, which Gardenhire expects them to do if that situation arises.
"We would have the ability to try to work something out, but I don't think that's going to happen," Gardenhire said. "Washington is probably going to take him back. So he's been traveling a little bit. It's a tough situation for the kid, but he needs to play."